Question

limit (1+(1/x^2))x as x approaches infinity

Answer 1

using L'Hopitals rule

Answer 2

This?\[
\lim_{x\to\infty}\left(1+\frac{1}{x^2}\right)x
\]

Answer 3

yes

Answer 4

I know the answer is infinity but I need to know how to do it with L'Hopital

Answer 5

So simplify the inner part a bit: \[
\left(1+\frac{1}{x^2}\right)x=\frac{x^2+1}{x}
\]

Answer 6

Divide everything by \(x\): \[
\frac{x+\frac 1x}{1}
\]

Answer 7

so its 2x/1 and then you get infinity

Answer 8

You don't need to use l'Hospitals rule on this one.

Answer 9

This goes to infinity and it isn't an indeterminate form.

Answer 10

yeah I know but I need to do it with L'Hopital

Answer 11

Okay, well you know how to do derivatives, I don't see the issue.

Answer 12

okay I just couldnt figure out how to get it in a form where I could do it in the end it was obvious lol. Thanks for the help.